# Sharp bounds of third Hankel determinant for a class of starlike functions and a subclass of q-starlike functions

Document Type : Original Article

Authors

Department of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi -110042

10.22034/kjm.2022.350982.2597

Abstract

Following the trend of coefficient bound problems in Geometric Function Theory, in the present paper, the authors obtain the sharp bound of third Hankel determinant for the classes $S^*$, of starlike functions and $SL^*_q$, of $q$-starlike functions related with lemniscate of Bernoulli. Bound on the functions in the initial class, apart from being sharp is also an improvement over the known existing bound and the bound on the latter class generalizes the prior known outcome. Further, the extremal functions of classes $S^*$ and $SL^*_q$ are deduced to prove the sharpness of these results.

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